{
 "cells": [
  {
   "cell_type": "code",
   "id": "initial_id",
   "metadata": {
    "collapsed": true,
    "ExecuteTime": {
     "end_time": "2025-02-14T09:07:22.498922Z",
     "start_time": "2025-02-14T09:07:19.126534Z"
    }
   },
   "source": [
    "import d2l\n",
    "import torch\n",
    "from torch.distributions import multinomial"
   ],
   "outputs": [],
   "execution_count": 1
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-02-14T09:07:32.464471Z",
     "start_time": "2025-02-14T09:07:32.359474Z"
    }
   },
   "cell_type": "code",
   "source": [
    "fair_probs = torch.ones([6]) / 6\n",
    "multinomial.Multinomial(1, fair_probs).sample()"
   ],
   "id": "2adac5df4fbc61a7",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([0., 0., 0., 0., 0., 1.])"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 2
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-02-14T09:07:39.392024Z",
     "start_time": "2025-02-14T09:07:39.374989Z"
    }
   },
   "cell_type": "code",
   "source": "multinomial.Multinomial(10, fair_probs).sample()",
   "id": "ad1fae1c2d34c7b9",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([0., 1., 1., 2., 5., 1.])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 3
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-02-14T09:07:48.894138Z",
     "start_time": "2025-02-14T09:07:48.875933Z"
    }
   },
   "cell_type": "code",
   "source": [
    "# 将结果存储为32位浮点数以进行除法\n",
    "counts = multinomial.Multinomial(1000, fair_probs).sample()\n",
    "counts / 1000  # 相对频率作为估计值"
   ],
   "id": "17050ccdd2b5c288",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([0.1660, 0.1660, 0.1690, 0.1670, 0.1660, 0.1660])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 4
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-02-14T09:08:15.120095Z",
     "start_time": "2025-02-14T09:08:15.102066Z"
    }
   },
   "cell_type": "code",
   "source": "counts = multinomial.Multinomial(10, fair_probs).sample((5,))",
   "id": "135754857f425d15",
   "outputs": [],
   "execution_count": 5
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-02-14T09:08:34.109403Z",
     "start_time": "2025-02-14T09:08:34.083354Z"
    }
   },
   "cell_type": "code",
   "source": "counts",
   "id": "2e42afbc0bea03d",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[1., 2., 2., 2., 2., 1.],\n",
       "        [5., 1., 0., 0., 2., 2.],\n",
       "        [1., 2., 2., 2., 1., 2.],\n",
       "        [4., 1., 0., 1., 3., 1.],\n",
       "        [3., 0., 4., 0., 2., 1.]])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 6
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-02-14T09:11:24.051902Z",
     "start_time": "2025-02-14T09:11:24.023952Z"
    }
   },
   "cell_type": "code",
   "source": [
    "cum_counts = counts.cumsum(dim=0)\n",
    "cum_counts"
   ],
   "id": "a1a7b99783a9b582",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[ 1.,  2.,  2.,  2.,  2.,  1.],\n",
       "        [ 6.,  3.,  2.,  2.,  4.,  3.],\n",
       "        [ 7.,  5.,  4.,  4.,  5.,  5.],\n",
       "        [11.,  6.,  4.,  5.,  8.,  6.],\n",
       "        [14.,  6.,  8.,  5., 10.,  7.]])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 7
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-02-14T09:18:02.038106Z",
     "start_time": "2025-02-14T09:18:01.669543Z"
    }
   },
   "cell_type": "code",
   "source": [
    "counts = multinomial.Multinomial(10, fair_probs).sample((500,))\n",
    "cum_counts = counts.cumsum(dim=0)\n",
    "estimates = cum_counts / cum_counts.sum(dim=1, keepdims=True)\n",
    "\n",
    "d2l.set_figsize((6, 4.5))\n",
    "for i in range(6):\n",
    "    d2l.plt.plot(estimates[:, i].numpy(),\n",
    "                 label=(\"P(die=\" + str(i + 1) + \")\"))\n",
    "d2l.plt.axhline(y=0.167, color='black', linestyle='dashed')\n",
    "d2l.plt.gca().set_xlabel('Groups of experiments')\n",
    "d2l.plt.gca().set_ylabel('Estimated probability')\n",
    "d2l.plt.legend()"
   ],
   "id": "8daa506974279748",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1e6900b1450>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
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